Related papers: Deterministic sketching for Krylov subspace method…

Randomized algorithms can be used to speed up the analysis of large datasets. In this paper, we develop a unified methodology for statistical inference via randomized sketching or projections in two of the most fundamental problems in…

It is shown in this paper that, almost all current prevalent iterative \mbox{methods} for solving linear system of equations can be classified as what we called extended Krylov subspace methods. In this paper a new type of iterative methods…

We investigate the regularizing behavior of an iterative Krylov subspace method for the solution of linear inverse problems in precisions lower than double. Recent works have considered the projection of iterated Tikhonov methods using…

Nowadays, many fields of study are have to deal with large and sparse data matrixes, but the most important issue is finding the inverse of these matrixes. Thankfully, Krylov subspace methods can be used in solving these types of problem.…

This work is about rounding error analysis of randomized CholeskyQR-type algorithms for sparse matrices. We often encounter QR factorization of the sparse matrices in many real problems. In this work, we focus on some typical…

This paper presents new quadrature rules for functions in a reproducing kernel Hilbert space using nodes drawn by a sampling algorithm known as randomly pivoted Cholesky. The resulting computational procedure compares favorably to previous…

Datasets that are terabytes in size are increasingly common, but computer bottlenecks often frustrate a complete analysis of the data. While more data are better than less, diminishing returns suggest that we may not need terabytes of data…

Algorithmic Gaussianization is a phenomenon that can arise when using randomized sketching or sampling methods to produce smaller representations of large datasets: For certain tasks, these sketched representations have been observed to…

Developing efficient solvers for large-scale multi-term linear matrix equations remains a central challenge in numerical linear algebra and is still largely unresolved. This paper introduces a methodology leveraging CUR decomposition for…

We propose a randomized algorithm with quadratic convergence rate for convex optimization problems with a self-concordant, composite, strongly convex objective function. Our method is based on performing an approximate Newton step using a…

Several problems in machine learning, statistics, and other fields rely on computing eigenvectors. For large scale problems, the computation of these eigenvectors is typically performed via iterative schemes such as subspace iteration or…

Block Krylov subspace methods (KSMs) comprise building blocks in many state-of-the-art solvers for large-scale matrix equations as they arise, e.g., from the discretization of partial differential equations. While extended and rational…

For linear systems $Ax=b$ we develop iterative algorithms based on a sketch-and-project approach. By using judicious choices for the sketch, such as the history of residuals, we develop weighting strategies that enable short recursive…

Count-sketch is a popular matrix sketching algorithm that can produce a sketch of an input data matrix X in O(nnz(X))time where nnz(X) denotes the number of non-zero entries in X. The sketched matrix will be much smaller than X while…

In this study, we consider the numerical solution of large systems of linear equations obtained from the stochastic Galerkin formulation of stochastic partial differential equations. We propose an iterative algorithm that exploits the…

Randomization has emerged as a powerful set of tools for large-scale matrix and tensor decompositions. Randomized algorithms involve computing sketches with random matrices. A prevalent approach is to take the random matrix as a standard…

The singular value decomposition (SVD) of large-scale matrices is a key tool in data analytics and scientific computing. The rapid growth in the size of matrices further increases the need for developing efficient large-scale SVD…

Randomized subspace approximation with "matrix sketching" is an effective approach for constructing approximate partial singular value decompositions (SVDs) of large matrices. The performance of such techniques has been extensively…

Building upon the rule-algebraic stochastic mechanics framework, we present new results on the relationship of stochastic rewriting systems described in terms of continuous-time Markov chains, their embedded discrete-time Markov chains and…

Krylov subspace methods are a powerful family of iterative solvers for linear systems of equations, which are commonly used for inverse problems due to their intrinsic regularization properties. Moreover, these methods are naturally suited…